7、分子动力学模拟基础汇总

Chapter3MolecularDynamicsSimulation3.1MolecularDynamics:TheIdeaWhatismoleculardynamics?Itisatechniquetocomputetheequilibriumandtransportpropertiesofaclassicalmany-bodysystem.Meansthatthenuclearmotionoftheconstituentparticlesobeysthelawsofclassicalmechanics.Newton’slaw,Lagrangianequation,andLangevinequation.Thisisanexcellentapproximationforawiderangeofmaterials.MDsimulationissimilartorealexperimentsWhenweperformarealexperiments,weproceed:Preparingasampleofthematerialstudied;Connectingthesampletoameasuringinstrument;Measuringthepropertyofinterestduringacertaintime;Ifthemeasurementsaresubjecttostatisticalnoise,thenthelongerweaverage,themoreaccurateourmeasurementbecomes.InaMDsimulation,wefollowexactlythesameapproach.e.g.,athermometer,manometer,orviscometer,etc.MDapproachFirst,prepareasample:selectamodelsystemconsistingofNparticles;Second,solveNewton’sequationofmotionuntilthepropertiesofthesystemnolongerchangewithtime.Interactionenergypotential,pairpotentialisfrequentlyusedEquilibratethesystemAfterequilibration,performtheactualmeasurement.SomeofthemostcommonmistakesinMDaresimilartothemistakesthatmaybemadeinrealexperiments.Thesampleisnotpreparedcorrectly,thetimeistooshort,thesystemundergoesanirreversiblechangeduringtheexperiment,orwedonotmeasurewhatwethink.Howtomeasureanobservablequantity?TomeasureanobservablequantityinaMDsimulation,wemustfirstofallbeabletoexpressthisobservableasafunctionofthepositionsandmomentaoftheparticlesinthesystem.Letustaketemperatureasanexample.Makinguseoftheequipartitionofenergyoveralldegreesoffreedom,Nf,wehave:21()()22NiiBfimvtkTtN21()()NiiiBfmvtTtkNTherelativefluctuationsinthetemperaturewillbeoforder.AsNfistypicallyoftheorderof102-103,thestatisticalfluctuationsareoftheorderof5-10%.1/fNAverageovermanyfluctuationsInwhichcaseshouldweworryaboutquantumeffects?Whenweconsiderthethetranslationalorrotationalmotionoflightatomsormolecules,orvibrationalmotionwithafrequencysuchthathkBT.He,H2,D2,etc.Ofcourse,ourcourseofthisvastsubjectisincomplete.Ifyouneedtheknowledgebeyondthecourse,youcanreadthereferencesonthecomingslide.ReferencesforMolecularDynamicsMPAllen&DJTildesley,1987,ComputerSimulationofLiquids.HCBerendsen&WFvanGunsteren,1984,MolecularDynamicsSimulations:Techniques&Approached,NATOASISeriesC123.CLBrooksetal.,1988,Proteins.ATheoreticalPerspectiveofDynamics,StructureandThermodynamics.AdvancesinchemicalPhysics.VolumeLXXI.JMHaile,1992,MolecularDynamicsSimulation.ElementaryMethods.4.2MolecularDynamics:AProgramThebestintroductiontoMDistoconsiderasimpleprogram.WekeepitassimpleaspossibletoillustratesomeimportantfeaturesofMD.Itisconstructedas:readintheparametersthatspecifytheconditionsoftherun(e.g.,initialtemperature,numberofparticles,density,timestep,etc.);Initializethesystem(selectinitialriandvi);Computetheenergyandforcesonallparticles;IntegrateNewton’sequationsofmotion;measurethequantitiesinthepresenttime;Aftercompletionofthecentralloop,computeandprinttheaveragesofmeasuredquantities,andstop.Centralloop,thecoreofthesimulationAsimpleMDprogramProgramMDsimpleMDprogramcallinitinitializationt=0settimedowhile(t.lt.tmax)MDloopcallforce(f,en)determinetheforcescallintegrate(f,en)integrateequationsofmotiont=t+deltupdatetimecallsamplesampleaveragesenddostopSubroutineinit,force,andintegratewillbedescribedlater.Subroutinesampleisusedtocalculateaveragesofquantitiesofinterestlikepressureandtemperature,etc.4.2.1InitiallizationTostartthesimulation,weshouldassigninitialpositionsandvelocitiestoallparticlesinthesystem.Oftenthisisachievedbyinitiallyplacingtheparticlesonacubiclattice.Avoidingpositionsthatresultinanappreciableoverlap;choosepositionscompatiblewiththestructurethatweareaimingtosimulate.Astheequilibriumpropertiesofthesystemdonotdependonthechoiceofinitialconditions,allreasonableinitialconditionsareinprincipleacceptable.InitialpositionsTosimulateasolidstateofamodelsystem,itislogicaltopreparethesysteminthecrystalstructureofinterest.Ifweareinterestinthefluidphase,wesimplypreparethesysteminanyconvenientcrystalstructure.Ifthedensityclosetothefreezing,selectionofcrystalstructureisunwise:meta-stableInitialpositionsrandomly;usefinalconfigurationofaliquidatahighertemperatureorlowerdensity.Howtoavoidit?Initialpositions---continueInanycases,itisusuallypreferabletousethefinalconfigurationofanearliersimulationatanearbystatepointasthestartingconfigurationforanewrunandadjustthetemperatureanddensitytothedesiredvalues.Well-equilibratedTheobservedvaluesshouldnotdependontheinitialcondition.Ifdoes,therearetwopossibilities:Thesystemreallybehavesnon-ergodically.Inglassymaterialsorlow-temperature,disorderedalloys.Samplingconfigurationspaceisinadequate---notyetreachequilibrium.Latticepositions(FCC)CCELL=LENGTH/REAL(NC)CELL2=0.5*CELLC**SUBLATTICEA**RX0(1)=0.0RY0(1)=0.0RZ0(1)=0.0C**SUBLATTICEB**RX0(2)=CELL2RY0(2)=CELL2RZ0(2)=0.0C**SUBLATTICEC**RX0(3)=0.0RY0(3)=CELL2RZ0(3)=CELL2C**SUBLATTICED**RX0(4)=CELL2RY0(4)=0.0RZ0(4)=CELL2ADBCCELLLENGTHC**CONSTRUCTTHELATTICEFROMTHEUNITCELL**M=0DO100IZ=1,NCDO100IY=1,NCDO100IX=1,NCDO110IREF=